What if you had an algebraic equation involving multiplication or division like
? How could you solve it for the unknown variable
x
? After completing this Concept, you'll be able to solve equations like this one.

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Guidance

Suppose you are selling pizza for $1.50 a slice and you can get eight slices out of a single pizza. How much money do you get for a single pizza? It shouldn’t take you long to figure out that you get
. You solved this problem by multiplying. Here’s how to do the same thing algebraically, using
to stand for the cost in dollars of the whole pizza.

Example A

Solve
.

Our
is being multiplied by one-eighth. To cancel that out and get
by itself, we have to multiply by the reciprocal, 8. Don’t forget to multiply
both sides
of the equation.

Example B

Solve
.

0.25 is the decimal equivalent of one fourth, so to cancel out the 0.25 factor we would multiply by 4.

Solving by division is another way to isolate
. Suppose you buy five identical candy bars, and you are charged $3.25. How much did each candy bar cost? You might just divide $3.25 by 5, but let’s see how this problem looks in algebra.

Example C

Solve
.

To cancel the 5, we divide both sides by 5.

Example D

Solve
.

Divide by 1.375

Notice the bar above the final two decimals; it means that those digits recur, or repeat. The full answer is 0.872727272727272....